Question

Marcy 的所有弹珠都是蓝色、红色、绿色或黄色。她的弹珠中三分之一是蓝色，四分之一是红色，且有六颗绿色弹珠。Marcy 最少可能有多少颗黄色弹珠？

All of Marcy's marbles are blue, red, green, or yellow. One third of her marbles are blue, one fourth of them are red, and six of them are green. What is the smallest number of yellow marbles that Marcy could have?

$1$

$2$

$3$

$4$

$5$

答案：D

知识点：分数最小公倍数

难度评级：1070

视频讲解：

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文字解答：

如果弹珠总数同时能被 $3$ 和 $4$ 整除，那么它必须能被 $12$ 整除。测试 $12$ 时，蓝色有 $4$ 颗，红色有 $3$ 颗，最多只剩 $5$ 颗绿色，不可能。

若总数为 $24$ ，则蓝色有 $8$ 颗，红色有 $6$ 颗。黄色弹珠数为 $24 - 8 - 6 - 6 = 4$ 。

所以正确答案是 D。

If the number of marbles is divisible by both $3$ and $4,$ then the number must be divisible by $12.$ If we test $12,$ we get that there are $4$ blue marbles and $3$ red marbles. This leaves a maximum of $5$ green marbles, which is not possible.

If there are $24$ marbles, then there are $8$ blue marbles and $6$ red marbles. To find the number of yellow marbles, we get $24 - 8 - 6 - 6 = 4.$

Thus, D is the correct answer.

2017 AMC 8 第 9 题

答案：D

难度评级：1070

视频讲解：

文字解答：

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